All Questions

A rather basic question. What was the original reason to consider the underlying $\mathbb{Z}$-module of the - as canonical object regarded - Tate-Hodge structure $\mathbb{Z}(1)$ to be given as $2 \pi ...

My question refers to a discussion from this older thread on Neron-Severi group of a Kähler manifold. In the comments below Ted Shifrin's answer there arose a discussion when the map $H^2(X,\mathbb{Z}...

Let $\eta$, $\omega$ be two $(1,1)$-forms on $\mathbb{C}^m \times Y$, where $Y$ is a compact Kahler manifold with vanishing first Chern class, i.e., a Calabi-Yau manifold. Suppose that for all $z \in \...

For an $2n$-dimensional complex manifold $M$, and a smooth vector bundle $E$ over $M$, it is well-known (see Voisin, Huybrechts) that there exists an operator $\overline{\partial}$, built locally from ...